Financial Risk & Return Analysis
Ivan and Yaren
Introduction
Let’s be honest—when it comes to investing, we’ve all wondered:
Should I put all my money into one strong stock, or is it smarter to diversify and spread the risk?
Or maybe you haven’t even asked that question yet—because you’re just getting started.
That’s exactly where this beginner-friendly analysis comes in.
Using three of the most well-known companies—Apple, Microsoft,
and Tesla—we’ve created a simple roadmap for anyone who’s
looking to take their first steps into the stock market or just wants to
better understand how it all works.
Before we dive in, let’s quickly go over how we’re calculating returns in this project. We’re using adjusted closing prices, because they reflect the real picture—they factor in things like dividends, stock splits, and other corporate changes. That way, we’re not fooled by artificial jumps or drops in price, and we can focus on what really matters: actual market movement.
From there, we calculate the daily return, which is just the change in price from one trading day to the next. It’s a simple but powerful way to track how a stock performs over time, spot volatility, and get a better sense of how efficient a portfolio really is.
Which Stock Has the Highest Risk?
“When you’re just starting to invest, one of the first questions you’re likely to ask is: ‘How risky is this stock?’ Because let’s face it—risk is just as much a part of the game as reward.”
Understanding Volatility
Volatility is a frequently encountered concept in the world of
finance and holds great importance for investors.
But what exactly is volatility?
Volatility refers to the degree of fluctuation in the price of a
financial asset.
In other words, it describes how quickly and significantly the price of
an asset changes.
For investors, volatility can imply risk and uncertainty. However, when managed with the right strategies, it can also present opportunities.
Volatility isn’t always bad — it’s a sign that the market is moving. Smart investors learn how to ride those waves rather than fear them.
Volatility matters because it helps investors align their portfolios with their personal risk tolerance.
There are several ways to measure volatility, but the most common method is the calculation of standard deviation. Standard deviation indicates how much an asset’s return deviates from its average. A high standard deviation signifies high volatility, while a low standard deviation indicates low volatility.
<<<<<<< HEADHigh volatility is often observed during periods of increased uncertainty and risk in the markets. During such times, prices can experience sudden and significant changes, which may amplify both potential gains and losses. Investors should closely monitor market movements during high-volatility periods and rebalance their portfolios if necessary. High volatility typically arises due to factors such as economic uncertainty, political events, natural disasters, or major company-specific developments.
Our data spans from 2019 to 2024, a period marked by major global events that likely influenced market volatility. These include the COVID-19 pandemic (2020), vaccine-driven recovery (2021), the Russia-Ukraine war (2022), global inflation and interest rate hikes (2022–2023), the AI stock rally (2023), and political and economic uncertainty in 2024. These events should be considered when interpreting volatility and asset performance.
To examine these effects more closely, we will use the volatility graph. This will allow us to compare the daily return variability of Apple, Microsoft, and Tesla more accurately, and better understand how each stock responded to market events during the 2019–2024 period.
During the first half of 2020, coinciding with the onset of the COVID-19 pandemic, all three stocks—AAPL, MSFT, and TSLA—experienced a sharp rise in volatility, reflecting heightened market uncertainty. As vaccines became available in early 2021, volatility declined noticeably, suggesting a return of investor confidence. The beginning of the Russia–Ukraine war in early 2022 triggered another local peak in volatility across all three stocks, followed by a gradual decline as markets adjusted to the new geopolitical reality.
Up to this point, the volatility trajectories of AAPL, MSFT, and TSLA remained broadly aligned, showing similar patterns of reaction and stabilization. However, after the emergence of AI-driven market narratives in 2023, a divergence began to appear. While AAPL and MSFT continued on a more stable and declining volatility path, TSLA’s volatility began to rise again—indicating a renewed period of elevated risk, possibly driven by speculation or sector-specific factors.
1.1 Maximum Drawdown
While volatility captures the fluctuations in returns, it does not reflect the magnitude of losses investors might endure. To address this limitation, we turn to the concept of Maximum Drawdown (MDD), MDD = (Trough Value - Peak Value) / Peak Value which measures the largest decline from a peak to a trough over the entire period. It reflects the most severe loss an investor could have faced.
SOMETHING WRONG HERE
## Maximum Drawdown of AAPL: 0.3142729## Maximum Drawdown of MSFT: 0.3714849## Maximum Drawdown of TSLA: 0.7363222The Maximum Drawdown results further confirm Tesla’s high-risk profile. While Apple and Microsoft experienced drawdowns of approximately 31% and 37% respectively, Tesla’s drawdown exceeded 73%. This indicates that during the worst observed period, Tesla investors could have faced a significantly deeper loss, highlighting the asset’s vulnerability to extreme downturns.
Historically, Tesla’s maximum drawdown has also been larger compared to Apple and Microsoft; according to one analysis, since 2010, Tesla stock has experienced a peak loss of around 61%, whereas Apple’s largest drawdown remained around 40%.
However, in finance, risk does not simply mean danger — it also represents opportunity. Higher risk can imply greater return potential, which is why many investors are still attracted to stocks like TSLA despite their volatility and drawdown profiles.
2 Which Stock Had the Highest Average Return?
Two commonly used methods are the arithmetic mean return and the geometric mean return, each with its advantages and limitations. The appropriate method should be selected based on the purpose and context of the analysis.
The arithmetic mean is calculated by adding up all daily or annual returns over a period and dividing the total by the number of observations. Due to its simplicity, it is widely used for short-term performance comparisons and return estimates.
2.1 Technology, Crisis, and Recovery
At the beginning of 2020, when COVID-19 brought the entire world to a standstill, uncertainty prevailed. But technology responded swiftly. Remote work, digital services, and electric vehicles surged — and Tesla soared. Microsoft and Apple, on the other hand, offered investors confidence through more cautious but steady growth.
When vaccines were developed, markets breathed a sigh of relief and stock prices climbed. However, new threats soon emerged: war, supply chain issues, and inflation. The year 2022 became a period of decline for all tech stocks, prompting investors to act more cautiously once again.
Then came 2023 — the rise of artificial intelligence. Microsoft stood out with its partnership with OpenAI. Tesla once again drew attention with its autonomous technologies. As always, Apple maintained its stability. Technology once again began to shape the future.
2.2 Risk–Return Trade-off
While Apple and Microsoft have maintained a more stable and balanced return profile throughout the period, Tesla has recorded both the highest and lowest returns in different time frames. These sharp fluctuations make Tesla the most illustrative example for understanding the relationship between risk and return.
In the first half of 2020, as the pandemic shook global markets, Tesla experienced a remarkable surge. Both its volatility and returns peaked. This was one of those periods where taking risk clearly paid off.
However, the same relationship did not always hold. In the first half of 2022, amidst geopolitical tensions and economic uncertainty, Tesla once again showed high volatility — but this time, returns turned negative. In other words, the same level of risk resulted in a loss instead of a gain.
By 2023, Tesla had regained strength. As the broader market recovered, its returns began to rise again. Taken together, these periods demonstrate that volatility can signal not only potential gains, but also the risk of significant losses.
3 Does diversification reduce risk?
There is a well-known saying often attributed to economist Harry Markowitz, the father of Modern Portfolio Theory:
“Diversification is the only free lunch in investing.”
Or, as people like to put it more casually: “Don’t put all your eggs in one basket.”
Diversification means spreading investments across different assets to reduce exposure to the risk of any single investment.
The basic idea is that not all assets move in the same direction at the same time.
By combining assets with different risk and return profiles, investors can potentially reduce the overall risk of their portfolio while maintaining reasonable return expectations.
The goal of diversification is to reduce overall volatility and achieve a more balanced return by combining assets with low correlation.
Correlation analysis is conducted to identify which assets, when combined in a portfolio, will have a risk-reducing effect.
Low correlation reduces portfolio volatility.
High correlation increases portfolio volatility.
## AAPL TSLA MSFT
## AAPL 1.0000000 0.4659280 0.7341606
## TSLA 0.4659280 1.0000000 0.4318455
## MSFT 0.7341606 0.4318455 1.0000000AAPL – TSLA = 0.47
A moderate positive relationship. Sometimes they move together, sometimes they don’t.AAPL – MSFT = 0.73
A strong positive relationship. They generally move in the same direction.TSLA – MSFT = 0.43
A moderate relationship. Sometimes they move similarly, but there is also a degree of independence.We will use these results to build our portfolio diversification strategy.
Assets with very high correlation (such as AAPL and MSFT) provide less diversification.
Assets with moderate or low correlation (such as TSLA and AAPL or TSLA and MSFT) provide better diversification.
The goal is to determine whether the assets added to the portfolio balance each other or tend to move in the same direction.
Our hypothesis is as follows:
Low Risk / Stability Objective:
A portfolio weighted 50% Microsoft and 50% Apple is expected to provide stable but limited returns due to its low volatility.Balanced Risk / Return Objective:
A portfolio weighted 50% Microsoft, 30% Apple, and 20% Tesla is expected to offer moderate returns with an acceptable level of risk.High Return / High Risk Objective:
A portfolio weighted 50% Tesla, 25% Apple, and 25% Microsoft is expected to deliver the highest potential returns, despite higher volatility.Maximum Sharpe Ratio Objective:
A portfolio weighted 85% Microsoft and 15% Tesla is expected to provide the highest return per unit of risk, maximizing the Sharpe Ratio.
##
## ==== Low Risk / Stability ====
## Annual Return: 44.82 %
## Annual Volatility: 33.95 %
## Sharpe Ratio: 1.32##
## ==== Balanced Risk / Return ====
## Annual Return: 39.03 %
## Annual Volatility: 30.54 %
## Sharpe Ratio: 1.28##
## ==== High Return / High Risk ====
## Annual Return: 51.48 %
## Annual Volatility: 40.84 %
## Sharpe Ratio: 1.26##
## ==== Maximum Sharpe Ratio ====
## Annual Return: 34.63 %
## Annual Volatility: 30.13 %
## Sharpe Ratio: 1.15Balanced Portfolio (50% MSFT – 30% AAPL – 20% TSLA)
Achieved the highest Sharpe ratio of 1.28, with an annual return of 39% and volatility of 30.5%.
This represents the best balance between risk and return.Low-Risk Portfolio (50% MSFT – 50% AAPL)
Stands out as the least risky option, offering a 32% annual return with relatively low volatility.High-Return Portfolio (50% TSLA – 25% AAPL – 25% MSFT)
Provides the highest potential return of 51.5% annually, but comes with high volatility of 40.8%, making it susceptible to significant fluctuations.Maximum Sharpe Portfolio (85% MSFT – 15% TSLA)
Appears theoretically efficient, but does not outperform the balanced portfolio in practice.Recommendation
- We recommend the 50% MSFT – 30% AAPL – 20% TSLA allocation as the optimal choice for investors seeking a strong balance between risk and return, supported by the best Sharpe ratio.
- For risk-averse investors, the 50% MSFT – 50% AAPL portfolio is suggested.
- For aggressive investors, the 50% TSLA-weighted portfolio could be considered, acknowledging its higher volatility.
- To better manage overall portfolio risk, reducing the weight of Tesla could be considered, while keeping Apple and Microsoft as stabilizing components to maintain diversification benefits.
We can prove this by calculating standard deviation both for diversified investment and single one and compare them. As we know, standard deviation considered to be a “Risk Marker”, so we expect diversified portfolio to have lower standard deviation score.
## Standard Deviation of AAPL: 0.019426## Standard Deviation of MSFT: 0.018265## Standard Deviation of TSLA: 0.04060822## Standard Deviation of Diversified Portfolio: 0.02174893As you can see, our diversified portfolio has 2% of Standard Deviation, meanwhile, AAPL and MSFT have 1.94% and 1.83% respectively. That means 2 things. 1 - I was wrong, Standard deviation of our portfolio is higher. 2 - AAPL and MSFT itself more safe asset to have.
Why then Mr. Markowitz was so desperate about diversification? And the answer is - return. Let me explain.
When we combine these three stocks into an equally weighted diversified portfolio, the portfolio’s standard deviation is 2.17%, which is lower than Tesla’s individual risk, but slightly higher than Apple’s or Microsoft’s risk.
This result demonstrates that diversification reduces the overall impact of the riskiest asset in the portfolio. Even though the portfolio still carries some risk, the extreme fluctuations of Tesla are balanced out by the relative stability of Apple and Microsoft.
Moreover, the potential return of the diversified portfolio remains attractive, since it still benefits from Tesla’s higher return potential while reducing its extreme downside risk.
Therefore, this example illustrates why diversification makes sense in practice: it helps to lower risk while preserving opportunities for higher returns.
Is simple terms, as we want our portfolio to grow, we can invest in risky assets to gain more and still consider our portfolio to be safe, using this.
Let me demonstrate it, using the following chart:
The Risk-Return Comparison chart illustrates how diversification helps to balance risk and return.
We can see that Tesla provides the highest average return (0.28%) but comes with the highest risk (4.06% standard deviation). On the other hand, Apple and Microsoft offer lower risk (around 1.8–1.9%) but also lower returns (around 0.11–0.14%).
The diversified portfolio, which combines all three stocks equally, achieves a higher return (0.18%) than Apple and Microsoft individually, while maintaining a moderate risk (2.17%), significantly lower than Tesla’s standalone risk.
This shows that diversification allows us to benefit from the growth potential of riskier assets like Tesla while keeping the overall risk at an acceptable level thanks to the stabilizing effect of safer assets like Apple and Microsoft.
In other words, diversification does not eliminate risk entirely, but it smooths the extremes, providing a more balanced and resilient portfolio that preserves the opportunity for higher returns without fully exposing the investor to the risks of any single stock.
To strengthen the analysis, we conducted two additional statistical tests: • T-Test: This test was used to check whether the difference in returns between Tesla and Apple is statistically significant. The results confirmed that Tesla’s returns are not significantly higher than Apple’s, with a p-value above 0.05, supporting the conclusion that Tesla offers nearly same potential returns but at a higher risk.(Askim, please check. Maybe I calculated it wrong. It shouldn’t be the same)
##
## Welch Two Sample t-test
##
## data: as.vector(returns_tsla) and as.vector(returns_aapl)
## t = 1.1788, df = 2163.8, p-value = 0.2386
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.0009065514 0.0036384989
## sample estimates:
## mean of x mean of y
## 0.002814698 0.001448724• Linear Regression: A regression analysis between Tesla’s returns and the diversified portfolio’s returns revealed a positive relationship. This indicates that Tesla’s performance has a measurable influence on the portfolio’s overall return, contributing to both its higher return and higher volatility. This supports the idea that adding a riskier asset like Tesla can boost portfolio performance while still maintaining a balanced risk profile thanks to diversification.regression_model <- lm(returns_tsla ~ portfolio_returns)
summary(regression_model)##
## Call:
## lm(formula = returns_tsla ~ portfolio_returns)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.15486 -0.01074 -0.00018 0.01057 0.09931
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0001613 0.0004944 -0.326 0.744
## portfolio_returns 1.6468657 0.0226633 72.667 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01914 on 1507 degrees of freedom
## Multiple R-squared: 0.778, Adjusted R-squared: 0.7778
## F-statistic: 5280 on 1 and 1507 DF, p-value: < 2.2e-16The linear regression results show a strong and statistically significant positive relationship between the returns of Tesla and the returns of the diversified portfolio.
Since the p-value is nearly 0, the probability of the result being an accident is extremely low. We can trust the result.
The coefficient of 1.65 indicates that Tesla’s returns amplify the portfolio’s movements, meaning Tesla behaves like a high-beta asset, increasing portfolio returns when the portfolio performs well, but also increasing losses when the portfolio performs poorly (higher volatility). That means that when our portfolio grows 1%, Tesla grows 1.65%.
With an R-squared of 77.8%, the model explains a large portion of Tesla’s return variability, confirming that Tesla’s performance is closely related to the portfolio’s overall dynamics. This reinforces the idea that adding Tesla to a diversified portfolio can boost returns, but it also makes the portfolio more sensitive to market movements. ⸻
| Stock | Maximum Drawdown |
|---|---|
| AAPL | -0.3143 |
| MSFT | -0.3715 |
| TSLA | -0.7363 |
The Maximum Drawdown results back up what we’ve already seen: Tesla carries a much higher level of risk. While Apple and Microsoft saw drawdowns of about 31% and 37%, Tesla’s drawdown was over 73% — a huge difference. This means that in the worst-case scenario, Tesla investors could have lost more than two-thirds of their investment value — showing just how sensitive the stock is to major downturns.
This isn’t new for Tesla. Looking further back, one analysis shows that since 2010, Tesla has faced a 61% peak loss, while Apple never dropped more than 40% in the same period.
Yes, Tesla’s ups and downs are bigger, but that’s also part of what makes it appealing. Higher risk often comes with the chance for higher returns — and for many investors, that’s a risk worth taking.
In the following section, we’ll take a closer look at how each stock actually performed.
Which Stock Had the Highest Average Return?
Arithmetic Mean Return and Geometric Mean Return
Before diving into the results, let’s clear something up. When it comes to measuring returns, there are two common methods: the arithmetic mean return and the geometric mean return. Each has its own strengths and weaknesses, and choosing the right one depends on what exactly you’re trying to analyze.
The arithmetic mean is calculated by adding up all daily (or annual) returns over a period and dividing the total by the number of observations. Because it’s simple and easy to interpret, it’s often used for short-term performance comparisons and quick return estimates.
In this analysis, we’ll use the arithmetic mean because our focus is on comparing the average performance of each stock over specific time intervals, rather than modeling long-term compounded growth.
Visualization: Average Returns Over Time
If you’ve followed along so far great! Let’s keep going.
In the previous section, we mentioned that risk can also lead to reward. So after seeing Tesla’s extreme volatility and massive drawdowns, you might be thinking:
“Well, with all that risk, I hope the returns are worth it!”
Let’s find out — using the same method we applied for volatility.
While Apple and Microsoft kept things relatively stable and steady throughout the period, Tesla stood out by swinging between the highest highs and the lowest lows. If you want to understand the relationship between risk and return, Tesla is the perfect example.
In the first half of 2020, as the pandemic shook the world, Tesla skyrocketed. Both its volatility and returns peaked. It was one of those moments where taking a risk really paid off.
But it didn’t always go that way. In the first half of 2022, with war and economic uncertainty in the air, Tesla was once again highly volatile — but this time, returns went negative. Same level of risk, very different outcome.
By 2023, Tesla was back on its feet. As the broader market started to recover, Tesla’s returns picked up again.
What all of this shows is simple: Volatility doesn’t just point to potential gains — it also warns us about possible losses.
Risk can reward you…
or remind you who’s in
charge.
Alright — now that things are starting to make a bit more sense, let’s go back to the question we asked at the very beginning:
Should I put all my money into one strong stock, or is it smarter to diversify and spread the risk?
Let’s take a closer look.
Does diversification reduce risk?
There is a well-known saying often attributed to economist Harry Markowitz, the father of Modern Portfolio Theory:
“Diversification is the only free lunch in investing.”
Diversification means spreading investments across different assets to reduce exposure to the risk of any single investment. The basic idea is that not all assets move in the same direction at the same time. By combining assets with different risk and return profiles, investors can potentially reduce the overall risk of their portfolio while maintaining reasonable return expectations. The goal of diversification is to reduce overall volatility and achieve a more balanced return by combining assets with low correlation.
Correlation analysis
Correlation analysis is conducted to identify which assets, when combined in a portfolio, will have a risk-reducing effect.
Low correlation reduces portfolio volatility.
High correlation increases portfolio volatility.
Here are the correlations between stocks that we calculated with the cor() function, using daily returns derived from the ROC() function in the {TTR} package.
| AAPL | TSLA | MSFT | |
|---|---|---|---|
| AAPL | 1.0000 | 0.4659 | 0.7342 |
| TSLA | 0.4659 | 1.0000 | 0.4318 |
| MSFT | 0.7342 | 0.4318 | 1.0000 |
Proposed Portfolio
The proposed portfolio allocation of 50% Microsoft, 30% Tesla, and 20% Apple is based on the observed correlation structure among the assets and the goal of achieving effective diversification.
Microsoft and Apple are highly correlated, which means they tend to move in the same direction. Allocating too much to both would reduce diversification benefits. Therefore, Microsoft is kept as the core low-volatility asset, while Apple’s weight is limited to avoid excessive overlap.
Tesla, on the other hand, has only moderate correlation with both Microsoft and Apple. Including Tesla at a moderate level (30%) enhances diversification and adds growth potential, without excessively increasing portfolio risk.
Method of Comparison
Shape Ratio :
The Sharpe ratio is one of the most widely used methods for measuring risk-adjusted relative returns. It compares a fund’s historical or projected returns relative to an investment benchmark with the historical or expected variability of such returns.
The higher the ratio, the higher the risk compensation an investment offers. Investors will therefore have a preference for investments with a high Sharpe ratio or investments that raise the entire portfolio’s Sharpe ratio through diversification.
Hypothesis
Our hypothesis is that the proposed portfolio (50% Microsoft, 30% Tesla, 20% Apple) offers a higher risk-adjusted return than both an equally weighted portfolio and any single-asset portfolio.
To test this, we will compare the Sharpe ratio of the proposed allocation against:
a random portfolio with equal weights across all three assets, and
fully concentrated portfolios consisting of only Microsoft, only Apple, or only Tesla.
These comparisons are made without relying on correlation structures, allowing us to assess whether the proposed weights themselves lead to a more efficient risk-return outcome.
| Portfolio | Sharpe Ratio |
|---|---|
| Proposed Portfolio | 1.32 |
|
Evenly Split Portfolio (Equal weights: 33% each) |
1.30 |
| 100% Tesla | 0.97 |
| 100% Apple | 1.10 |
| 100% Microsoft | 1.16 |
Which Portfolio Performs Best?
As expected, the proposed portfolio (50% MSFT – 30% TSLA – 20% AAPL) achieved the highest Sharpe ratio (1.32) among all compared strategies, confirming our hypothesis that this allocation provides the most efficient return relative to the risk taken.
The Evenly Split Portfolio, which distributes capital equally across all three assets without considering their risk characteristics, follows closely with a Sharpe ratio of 1.30, but falls slightly behind in efficiency.
All single-asset portfolios (100% in either Tesla, Apple, or Microsoft) perform worse in terms of risk-adjusted return:
Tesla shows the lowest Sharpe ratio (0.97) due to its high volatility and drawdown,
Apple (1.10) and Microsoft (1.16) perform better individually but lack the benefits of diversification.
These results confirm that strategic asset allocation, rather than equal weighting or concentration in a single asset, leads to better risk-adjusted performance.
Recommendation
While the proposed portfolio (50% Microsoft, 30% Tesla, 20% Apple) achieved the highest Sharpe ratio in our analysis, it is important to emphasize that there is no universally ideal portfolio. The optimal allocation depends not only on numerical performance metrics but also on the investor’s individual risk tolerance, goals, and personal preferences.
For example, an investor with a high risk appetite may reasonably prefer a higher allocation to Tesla, accepting greater volatility in exchange for potentially higher returns. In contrast, a more conservative investor might prioritize stability and allocate more heavily to Microsoft or Apple.
Therefore, we recommend that portfolio construction should not be based solely on statistical indicators such as the Sharpe ratio. Instead, investors should take into account their own investment personality, time horizon, and financial goals. Quantitative results can inform decision-making—but they should be used as a guide, not as a rule.
Sources
Apple vs. Tesla: Which Growth Stock to Own? — TheStreet
https://www.thestreet.com/apple/stock/apple-vs-tesla-which-growth-stock-to-ownBreaking Down the Geometric Mean — Investopedia
https://www.investopedia.com/articles/investing/071113/breaking-down-geometric-mean.aspTesting ChatGPT: Arithmetic vs. Geometric Returns — TheStreet Retirement Daily
https://www.thestreet.com/retirement-daily/your-money/testing-chatgpt-arithmetic-vs-geometric-returnsHarry Markowitz and Modern Portfolio Theory — Corporate Finance Institute
https://corporatefinanceinstitute.com/resources/career-map/sell-side/capital-markets/harry-markowitz/Sharpe Ratio — Investopedia
https://www.investopedia.com/terms/s/sharperatio.aspTesla-meme — 9GAG
https://9gag.com/tag/cybertruck